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NuclearChemistry

Chapter 21Nuclear Chemistry

Chemistry, The Central Science, 10th editionTheodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten

John D. BookstaverSt. Charles Community College

St. Peters, MO 2006, Prentice Hall, Inc.

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NuclearChemistry

The Nucleus

• Remember that the nucleus is comprised of the two nucleons, protons and neutrons.

• The number of protons is the atomic number.• The number of protons and neutrons together

is effectively the mass of the atom.

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NuclearChemistry

Isotopes

• Not all atoms of the same element have the same mass due to different numbers of neutrons in those atoms.

• There are three naturally occurring isotopes of uranium:�Uranium-234�Uranium-235�Uranium-238

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NuclearChemistry

Radioactivity

• It is not uncommon for some nuclides of an element to be unstable, or radioactive.

• We refer to these as radionuclides.• There are several ways radionuclides

can decay into a different nuclide.

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NuclearChemistry

Nuclear Equations

• In a nuclear reaction the atomic mass and atomic number has to add up in the reactants and the products.

U23892

→ Th23490 He4

2+

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NuclearChemistry

What product is formed when radium-226 undergoes alpha decay?P

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NuclearChemistry

What product is formed when radium-226 undergoes alpha decay?

Which element undergoes alpha decay to form lead-208?

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NuclearChemistry

Alpha Decay:

Loss of an α-particle (a helium nucleus)

He42

U23892

→ Th23490 He4

2+

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NuclearChemistry

Beta Decay:

Loss of a β-particle (a high energy electron)

β0−1 e0

−1or

I13153 Xe131

54→ + e0−1

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NuclearChemistry

Positron Emission:Loss of a positron (a particle that has the same mass as but opposite charge than an electron)

What actually happens is :

e01

C116

→ B115 + e0

1

1 1 01 0 1p n + e→

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NuclearChemistry

Gamma Emission:

Loss of a γ-ray (high-energy radiation that almost always accompanies the loss of a nuclear particle)

γ00

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NuclearChemistry

Electron Capture (K-Capture)

Addition of an electron to a proton in the nucleus�As a result, a proton is transformed into a neutron.

p11 + e0

−1 → n10

81 0 8137 1 36Rb + (orbital electron) Kr e− →

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NuclearChemistry

Where does nuclear energy come from?

E = mc2

n3CsRbUn 10

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10 ++→+

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NuclearChemistry

• Neutron proton ratio is nothing but the ratio between the number of protons and neutrons

• Number of neutrons= mass number –atomic number

Atomic number = number of protonsMass number = number of protons +

neutrons

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NuclearChemistry

Neutron-Proton Ratios

• Any element with more than one proton (i.e., anything but hydrogen) will have repulsions between the protons in the nucleus.

• A strong nuclear forcehelps keep the nucleus from flying apart.

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NuclearChemistry

Neutron-Proton Ratios

• Neutrons play a key role stabilizing the nucleus.

• Therefore, the ratio of neutrons to protons is an important factor.

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NuclearChemistry

Neutron-Proton Ratios

For smaller nuclei (Z ≤ 20) stable nuclei have a neutron-to-proton ratio close to 1:1.

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NuclearChemistry

Neutron-Proton Ratios

As nuclei get larger, it takes a greater number of neutrons to stabilize the nucleus.

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NuclearChemistry

Stable Nuclei

The shaded region in the figure shows what nuclides would be stable, the so-called belt of stability.

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NuclearChemistry

• Nuclei above this belt have too many neutrons.

• They tend to decay by emitting beta particles.

I13153 Xe131

54→ + e0

−1

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NuclearChemistry

• Nuclei below the belt have too many protons.

• They tend to become more stable by positron emission or electron capture.

p11 + e0

−1 → n10

C116

→ B115 + e0

1

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NuclearChemistry

Predict the mode of decay of (a) carbon-14, (b) xenon-118.

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NuclearChemistry

Predict the mode of decay of (a) carbon-14,

(b) (b) xenon-118.

(b) Xenon has an atomic number of 54. Thus, xenon-118 has 54 protons and 118 – 54 = 64 neutrons, giving it a neutron-to-proton ratio of According to Figure 21.2, stable nuclei in this region of the belt of stability have higher neutron-to-proton ratios than xenon-118. The nucleus can increase this ratio by either positron emission or electron capture:

Solve: (a) Carbon has an atomic number of 6. Thus, carbon-14 has 6 protons and 14 –6 = 8 neutrons, giving it a neutron-to-proton ratio of Elements with low atomic numbers normally have stable nuclei with approximately equal numbers of neutrons and protons. Thus, carbon-14 has a high neutron-to-proton ratio, and we expect that it will decay by emitting a beta particle:

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NuclearChemistry

Stable Nuclei

• There are no stable nuclei with an atomic number greater than 83.

• These nuclei tend to decay by alpha emission.

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NuclearChemistry

Radioactive SeriesOr

Nuclear Degenerative Series

• Large radioactive nuclei cannot stabilize by undergoing only one nuclear transformation.

• They undergo a series of decays until they form a stable nuclide (often a nuclide of lead).

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NuclearChemistry

Some Trends

Nuclei with 2, 8, 20, 28, 50, or 82 protons or 2, 8, 20, 28, 50, 82, or 126 neutrons tend to be more stable than nuclides with a different number of nucleons. These numbers are called magic numbers.Paired neutrons and protons have a special stability something like the paired electrons have a special stability

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NuclearChemistry

Some Trends

Nuclei with an even number of protons and neutrons tend to be more stable than nuclides that have odd numbers of these nucleons.

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NuclearChemistry

• In the radioactive series all the elements end in a Pb nucleus which has the magic number of 82

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NuclearChemistry

Nuclear Transformations

• Rutherford in 1919 performed the first nuclear transformation.

• The transmutations are sometimes represented by listing in order, the target nucleus, the bombarding particle, the ejecting particle and the product nucleus.

• The above equation becomes:

14 2 17 17 4 8 1N + He O + H→

14 17 7 8N( ,p) Oα

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NuclearChemistry

Write the balanced nuclear equation for the process summarized as

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NuclearChemistry

Nuclear Transformations

Nuclear transformations can be induced by accelerating a particle and colliding it with the nuclide in particle accelerators called cyclotrons or synchrotrons or particle smashers.

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NuclearChemistry

Particle Accelerators

These particle accelerators are enormous, having circular tracks with radii that are miles long.

Fermi National Accelerator Laboratory, Batavia, Illinois

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NuclearChemistry

• The synthetic isotopes used in medicine are synthesized using neutrons as the projectiles. Since neutrons are neutral they do not need to be accelerated to overcome the electrostatic repulsion of the nucleus.

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NuclearChemistry

• Cobalt-60 used in cancer therapy is made by the following reaction:

5826Fe + 1 0 n � 56

26 Fe

5626 Fe � 59

27 Co + 0 -1 e

5927 Co + 1 0 n � 60

27 Co

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NuclearChemistry

Transuranium Elements

• Artificial elements that have been produced in labs

• These have an atomic number above 92.

• They are short lived. • Elements 113 and 114 have not even

been assigned a name or symbol.

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NuclearChemistry

Kinetics of Radioactive Decay

• Nuclear transmutation is a first-order process.• The kinetics of such a process, you will recall, obey this equation:

• We can substitute the number of nuclei for concentration:

= -ktNtN0

ln

ln[A]t[A]0

= −kt

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NuclearChemistry

Kinetics of Radioactive Decay

• The half-life of such a process is:

= t1/20.693

k

• Comparing the amount of a radioactive nuclide present at a given point in time with the amount normally present, one can find the age of an object.

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NuclearChemistry

The half-life of cobalt-60 is 5.3 yr. How much of a 1.000-mg sample of cobalt-60 is left after a 15.9-yr period?

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NuclearChemistry

The half-life of cobalt-60 is 5.3 yr. How much of a 1.000-mg sample of cobalt-60 is left after a 15.9-yr period?

• Answer 0.125 mg

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NuclearChemistry

Kinetics of Radioactive Decay

A wooden object from an archeological site is subjected to radiocarbon dating. The activity of the sample that is due to 14C is measured to be 11.6 disintegrations per second. The activity of a carbon sample of equal mass from fresh wood is 15.2 disintegrations per second. The half-life of 14C is 5715 yr. What is the age of the archeological sample?

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NuclearChemistry

Kinetics of Radioactive Decay

First we need to determine the rate constant, k, for the process.

= t1/20.693

k

= 5715 yr 0.693

k

= k0.693

5715 yr

= k1.21 × 10−4 yr−1

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NuclearChemistry

Kinetics of Radioactive Decay

Now we can determine t:

= -ktNtN0

ln

= -(1.21 × 10−4 yr−1) t11.615.2ln

= -(1.21 × 10−4 yr−1) tln 0.763

= t2235 yr

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NuclearChemistry

A rock contains 0.257 mg of lead-206 for every milligram of uranium-238. The half-life for the decay of uranium-238 to lead-206 is 4.5 × 109 yr. How old is the rock?

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NuclearChemistry

A rock contains 0.257 mg of lead-206 for every milligram of uranium-238. The half-life for the decay of uranium-238 to lead-206 is 4.5 × 109 yr. How old is the rock?

1. Find the original amount of U 238 1 mg + 238 g/atom x 0.257 mg = (1.297mg)

206 g/atom

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NuclearChemistry

A rock contains 0.257 mg of lead-206 for every milligram of uranium-238. The half-life for the decay of uranium-238 to lead-206 is 4.5 × 109 yr. How old is the rock?

1. Find the original amount of U 238 1 mg + 238 g/atom x 0.257 mg = (1.297mg)

206 g/atom

2. Calculate k fromk = 0 .692 = 0.692 =(1.5 x 10 -10 / yr)

t ½ 4.5 x 109 years

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NuclearChemistry

`A rock contains 0.257 mg of lead-206 for every milligram of uranium-238.

The half-life for the decay of uranium-238 to lead-206 is 4.5 × 109 yr. How old is the rock?

1. Find the original amount of U 238 1 mg + 238 g/atom x 0.257 mg = (1.297mg)

206 g/atom

2. Calculate k fromk = 0 .692 = 0.692 =(1.5 x 10 -10 / yr)

t ½ 4.5 x 109 years

3. Calculate t from

t = - 1 ln Nt = 1.7x 10 9 yearsk N0

= -ktNtN0

ln

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NuclearChemistry

Measuring Radioactivity

• One can use a device like this Geiger counter to measure the amount of activity present in a radioactive sample.

• The ionizing radiation creates ions, which conduct a current that is detected by the instrument.

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NuclearChemistry

Energy in Nuclear Reactions

• There is a tremendous amount of energy stored in nuclei.

• Einstein’s famous equation, E = mc2, relates directly to the calculation of this energy.

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NuclearChemistry

Energy in Nuclear Reactions

• In the types of chemical reactions we have encountered previously, the amount of mass converted to energy has been minimal.

• However, these energies are many thousands of times greater in nuclear reactions.

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NuclearChemistry

Energy in Nuclear Reactions

For example, the mass change for the decay of 1 mol of uranium-238 is −0.0046 g.

The change in energy, ∆E, is then

∆E = (∆m) c2

∆E = (−4.6 × 10−6 kg)(3.00 × 108 m/s)2

∆E = −4.1 × 1011 J

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NuclearChemistry

Nuclear Fission

• How does one tap all that energy?• Nuclear fission is the type of reaction carried

out in nuclear reactors.

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NuclearChemistry

Nuclear Fission

• Bombardment of the radioactive nuclide with a neutron starts the process.

• Neutrons released in the transmutation strike other nuclei, causing their decay and the production of more neutrons.

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NuclearChemistry

Nuclear Fission

This process continues in what we call a nuclear chain reaction.

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NuclearChemistry

Nuclear Fission

If there are not enough radioactive nuclides in the path of the ejected neutrons, the chain reaction will die out.

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NuclearChemistry

Nuclear Fission

Therefore, there must be a certain minimum amount of fissionable material present for the chain reaction to be sustained: Critical Mass.

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NuclearChemistry

Nuclear Reactors

In nuclear reactors the heat generated by the reaction is used to produce steam that turns a turbine connected to a generator.

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NuclearChemistry

Nuclear Reactors

• The reaction is kept in check by the use of control rods.

• These block the paths of some neutrons, keeping the system from reaching a dangerous supercritical mass.

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NuclearChemistry

Nuclear Fusion

• Fusion would be a superior method of generating power.�The good news is that the

products of the reaction are not radioactive.

�The bad news is that in order to achieve fusion, the material must be in the plasma state at several million kelvins.

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NuclearChemistry

Nuclear Fusion

• Tokamak apparati like the one shown at the right show promise for carrying out these reactions.

• They use magnetic fields to heat the material.

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